Chaos Data Analyzer
Frequently Asked Questions

What is Chaos Data Analyzer?

Chaos Data Analyzer (CDA and CDA:Pro) are peer-reviewed DOS programs that read a disk file of numerical data (a time series) and perform various tests with the goal of detecting hidden determinism (chaos) and quantifying any such determinism that it finds. The files are standard ASCII text either supplied by the user or one of the built-in samples. Thus CDA is both a research and learning tool.

Precisely what tests can CDA perform?

Here's a list of the tests included in the regular version (1.0) of CDA:

• Data Manipulation: Allows you to remove alternate data points, differentiate, integrate, or smooth the data prior to analysis.
• Graph of Data: Allows you to plot the data versus time or to plot each data point versus its predecessor or two predecessors.
• Probability Distribution: Produces a histogram of the data values on a linear or logarithmic scale, ranks the data from lowest to highest, and estimates the value associated with an unstable fixed point.
• Polynomial Fit: Performs a least squares fit to a polynomial of any degree from 0 to 9.
• Power Spectrum: Performs a fast Fourier transform on the data and displays the power spectrum on a linear, log-linear, or log-log scale.
• Dominant Frequencies: Uses the maximum-entropy (or all poles) method of Press, et. al. in Numerical Recipes to determine the power spectrum, identify the dominant frequency component, and make a linear prediction of the next 18 terms in the series.
• Lyapunov Exponent: Calculates the largest Lyapunov exponent using the method of Wolf, et. al. in Physica D 16, 285 (1985).
• Capacity Dimension: Estimates the Hausdorff dimension of the time-lagged time series by the box-counting method as described in most texts on fractals.
• Correlation Dimension: Estimates the correlation dimension using the method of Grassberger and Procaccia in Physica D 13, 34 (1984).
• Correlation Function: Plots the autocorrelation function versus time lag.
• Correlation Matrix: Calculates the 3 largest orthogonal eigenfunctions of the time-lagged data, displays them in various ways, fits them to a set of model equations using the method of Rowlands and Sprott in Physica D 58, 251 (1992), and solves the model equations to make a nonlinear prediction of the next 18 terms in the series.
• Phase-Space Plots: Plots each data point versus its time derivative and versus its first and second time derivative.
• Return Maps: Plots the local maximum or minimum of the time series versus the previous maximum or minimum or the value of the time derivative at the time for which the time series crosses its average value.
• Poincare Movies: Plots every n-th data point versus its m-th predecessor in an animation (stroboscopic view).

What is the difference between CDA and CDA:Pro?

A Professional Version (2.2) of CDA (CDA:Pro) is also available. It contains about twice as many tests, including everything that is in the regular version of CDA. It is faster, will accommodate up to 32,000 data points, and includes thirty-six additional sample data sets. A detailed list of the differences between the two programs is available.

Can CDA be used by someone who is not mathematically inclined or familiar with the principles of chaos?

CDA was originally designed as a teaching and learning tool for those who have had little experience with chaos and nonlinear data analysis.  There is an automatic mode in which all the tests are performed sequentially and the results summarized on a single page.  However, analysis of chaotic data is not an exact science, and users should be prepared to devote time to developing analysis skills.  The program comes with many sample data sets and a tutorial to facilitate this process.

Can CDA be used to analyze multivariate data?

CDA will not directly analyze data in which several simultaneous quantities have been recorded (multivariate data). However, if you generate a univariate time series by entering the multivariate data sequentially, most of the tests will still work and will reveal and quantify any underlying determinism. The program can also read every other data point from a file, allowing you to ignore one of two recorded variables.

In what format must the data be provided?

CDA expects data files to be a single series of ASCII values delimited by a space, comma, carriage return, or line feed. The data can be in integer, floating point, decimal, hexadecimal, octal, or binary format. Data values should be in the range -10¹⁸ to +10¹⁸. If the data file is larger than can be accommodated, the data record is truncated, and a warning message appears. Optionally, the program allows every second, fourth, eighth, etc. data point to be read from a time series that exceeds the memory capacity of the program.

How many data points are required for CDA to give a meaningful assessment of the data?

There is no unique answer to this question, but a good rule of thumb is given in Tsonis' book, Chaos: From Theory to Application, where he argues that the number of required data points is approximately 10^{2 + 0.4D}, where D is the minimum dimension in which the attractor can be embedded (usually the next integer larger than the fractal dimension of the attractor for low-dimensional cases). Thus 16,382 data points (the maximum) should permit the analysis of attractors that can be embedded in up to about 5 dimensions. CDA:Pro with 32,000 data points should work up to about 6 dimensions.

Is there a way to analyze more than 16,382 data points?

The regular version of the program is limited to 16,382 data points. This is a consequence of a compiler limitation that requires data arrays to fit into one 64 K block of memory. The Professional Version of the program (CDA:Pro) allows up to 32,000 points. At this value the limit is due to the fact that DOS programs have to fit into 640 K of memory, and CDA is a large program that remains resident in memory to achieve maximum speed. DOS programs can be made to access expanded memory, but that would slow the calculations considerably. CDA does allow you to reduce the size of your data record to a tolerable value by successively taking alternate data points. The analysis of very large data records would be intolerably slow in many cases.

How long does the computer take to do the calculations?

Most of the calculations are nearly instantaneous on a modern PC. The slowest calculation is the correlation dimension, which takes about 2 minutes on a 120-MHz Pentium for a data set of 2000 points, but in that time, you get values for all embedding dimensions up to 10. The time required for the correlation dimension calculation scales as the square of the number of data points.

Can CDA be used to make predictions (i.e., the stock market)?

Making near-term predictions is one of the important applications of CDA. Since chaotic systems are deterministic, such predictions are possible in principle, even for seemingly random data. Long-term predictions are generally not possible, however, because of the sensitivity to initial conditions. CDA includes a linear predictor based on Fourier analysis and a nonlinear predictor based on principal-component analysis. CDA:Pro has two additional predictors, one based on an artificial neural net and one based on state-space averaging. Sample stock market and climatological data are included for practice. Of course, there are no guarantees of success in the stock market.

Can CDA be used to analyze automatically a large collection of data files?

CDA can be launched by another program or even a DOS batch file with all the necessary parameters to automate the analysis of a collection of data files.  In addition, CDA:Pro allows you to save the summary screen to a disk file, which can then be read by your calling program when CDA exits.  Of course, this requires you to do some programming outside of CDA.

Why are there differences in some of the values calculated by CDA and by CDA:Pro?

Many of the routines such as the correlation dimension calculation were completely rewritten in CDA:Pro to improve calculation speed, to allow larger data sets, and to prevent spurious results due to temporal correlation for oversampled data. These changes cause slight differences to be reported by the two programs for the same data sets. The differences should generally be within the stated error tolerances. If you are troubled by these differences, you are probably ascribing more significance to the calculated values than is warranted by your data.

Is CDA year 2000 compliant?

CDA and CDA:Pro are fully year 2000 compliant, and always have been.  The only use CDA makes of the date is to display it on the opening menu screen.

Is CDA compatible with Windows 9x,Windows NT, Windows 2000, Windows XP, Vista, Windows 7-10, etc.?

CDA and CDA:Pro are DOS programs and thus will run under any operating system that supports DOS including Windows 95 and 98, Windows NT, Windows 2000, Windows XP, and Windows 7-10. If you are using a recent version of Windows or are otherwise having trouble accessing "full screen mode", you will need to install D-Fend Reloaded (or another DOSBox front end) for Windows available free at http://dfendreloaded.sourceforge.net/.

Can screens from CDA be printed or saved to the clipboard?

CDA does not have built-in screen-print capability. However, in many cases you can do this using the Print-Screen key on your keyboard. This capability has become increasingly difficult with each new Windows release. There are third-party programs, including some freeware, that restore this capability to Windows XP, Vista, and Windows 7 such as D-Fend Reloaded (or another DOSBox front end) for Windows. The screen that contains the summary of the test results can be saved to a formatted text file on your hard disk and read by any text editor such as Notepad or Microsoft Word.

CDA is only available in a DOS version, and there are no plans to port it to other platforms. Because of the way the program is written and optimized for speed, such a port would be extremely difficult. The program will run on the Macintosh or Power Mac under SoftPC or SoftWindows, although some of the tests are slow for data sets larger than a few thousand points.

Is the source code available for CDA?

CDA was written in PowerBASIC in order to achieve speeds unobtainable in other languages. The code is in several dozen modules with many special and non-obvious programming tricks. It was never intended that the source code would be seen by anyone but the author, and consequently it is not consistently well structured and commented. It would be very difficult for someone not well familiar with the code to do anything useful with it, besides which, CDA is a commercial product. Consequently, the source code has never been and probably never will be released.

Is there a demo version of CDA?

A very limited demo version (1.0) of CDA can be downloaded from https://sprott.physics.wisc.edu/cdadem.exe. This program only allows you to make graphs of a single built-in data set (2000 data points from the logistic equation). The program has no expiration date and is intended to allow you to examine the user interface and to verify compatibility with your computer.  The full program is not available for downloading.

Where can I find more detail about the tests used in CDA?

If the information in the User's Manual is not sufficient for you, all of the tests used in CDA and the theory behind them along with references to the original literature are included in the book Chaos and Time-Series Analysis available from Oxford University Press (2003) and many other sources such as Amazon.com.

The program was previously distributed by Physics Academic Software, but it is no longer available from them. However, CDA:Pro can still be purchased directly from the author at half price ($150) as is without written documentation or technical support.

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